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Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map S S symmetry Article Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map Birgitta Dresp-Langley 1,* and John M. Wandeto 2 1 ICube Lab UMR 7357 CNRS, Strasbourg University, 67085 Strasbourg, France 2 Department of Information Technology, Dedan Kimathi University of Technology, Box 12405-10109 Nyeri, Kenya; [email protected] * Correspondence: [email protected] Abstract: Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. To this end, we exploit a neural network metric in the output of a biologically inspired Self- Organizing Map Quantization Error (SOM-QE). Shape pairs with perfect geometry mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within and/or across the shapes in a given pair produce, as shown here, a longer choice response time (RT) for “yes” responses relative to symmetry. These data are consistently mirrored by the variations in the SOM-QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data. Citation: Dresp-Langley, B.; Wandeto, J.M. Human Symmetry Keywords: symmetry; shape; local color; self-organized visual map; quantization error; SOM-QE; Uncertainty Detected by a choice response time; human decision; uncertainty Self-Organizing Neural Network Map. Symmetry 2021, 13, 299. https://doi.org/10.3390/sym13020299 1. Introduction Academic Editor: Janghoon Yang Received: 17 January 2021 Symmetry in biological and physical systems is a product of self-organization [1] driven Accepted: 8 February 2021 by evolutionary processes and/or mechanical systems under constraints. It conveys a basic Published: 10 February 2021 feature to living objects, from molecules to animal bodies, or to physical forces acting in synergy to create symmetrical structures [1–6]. In pattern formation, perfect symmetry is Publisher’s Note: MDPI stays neutral a regularity within a pattern, the two halves of which are mirror images of each other. In with regard to jurisdictional claims in information theory and in particular human information processing [7–11], symmetry is con- published maps and institutional affil- sidered an important carrier of information, detected universally by humans from an early iations. age on [12,13]. Human symmetry detection [14,15] in patterns or shapes involves visual and cognitive processes from lower to higher levels of functional organization [16–24]. Ver- tical mirror symmetry is a particularly salient form of visual symmetry [23–25], processed at early stages in human vision and producing greater or lesser detection reliability [23] Copyright: © 2021 by the authors. depending on local features of the stimulus display with greater or lesser stimulus certainty. Licensee MDPI, Basel, Switzerland. Shape symmetry is a visual property that attracts attention [18] and determines perceived This article is an open access article volume [19–22] and perceptual salience [26] of objects represented in the two-dimensional distributed under the terms and image plane. Aesthetic judgment and choice preference [27,28] are influenced by symmetry, conditions of the Creative Commons justifying biologically inspired models of symmetry perception in humans [29] under the Attribution (CC BY) license (https:// light of the fact that symmetry is detected not only by primates but also by other species, creativecommons.org/licenses/by/ such as insects, for example [30]. 4.0/). Symmetry 2021, 13, 299. https://doi.org/10.3390/sym13020299 https://www.mdpi.com/journal/symmetry Symmetry 2021, 13, 299 2 of 15 Symmetry may be exploited in pattern detection and classification by neural networks, which may have to learn multiple copies of the same object representation displayed in different orientations. Encoding symmetry as a prior shape in the network can, therefore, help avoid redundant computation where the network has to learn to detect the same pattern or shape in multiple orientations [31]. Symmetry-based feature extraction and/or representation [32] by neural networks using deep learning can, for example, help discover the most informative representations in large image databases with only a minor amount of preprocessing [33]. However, despite significant achievements of artificial intelligence in recognition and classification of well-reproducible patterns, the problem of uncertainty still requires additional attention, especially in ambiguous data. An artificial neural network that detects uncertainty states, where a human observer doubts about an image interpreta- tion has been described previously for the case of MagnetoEncephaloGraphic (MEG) image data with significant ambiguity [34]. Here in this study, we present an artificial neural network that detects uncertainty states in human observers with regard to shape symmetry. To this end, we exploit a neural network metric in the output of a biologically inspired Self-Organizing Map (SOM). The Quantization Error of the SOM (SOM-QE) [35–43] is a measure of output variance and quantifies the difference between neural network states at different stages of unsupervised image learning. In our previous studies, we demonstrated functional properties of the SOM-QE such as a sensitivity to the spatial extent, intensity, and sign or color of local image contrasts in unsupervised image classification by the neural network. The metric reliably detects the finest, clinically or functionally relevant variations in local image contrast contents [36–43], often invisible to the human eye [38,39,42,43]. Here it will be shown that the SOM-QE as a neural network state metric reliably captures, or correlates with, varying levels of human uncertainty in the detection of symmetry of shape pairs with varying local color information contents. Previous work using human two-alternative forced choice decision has shown that local color variations in two-dimensional pattern displays may significantly influence per- ceived relative distances [44–47]. In the present study, we use shapes that display perfect geometrical vertical mirror symmetry, as described further below here in Section 2.1, where visual uncertainty about symmetry is introduced by systematic variations in color (hue) and or saturation of local shape elements, leading to lesser or greater amounts of visual information content. The psychophysically determined choice response time, previously shown to directly reflect stimulus uncertainty in terms of a biological or physiological system states [48,49], is exploited as measure of symmetry uncertainty. Response time (RT) measurement is the psychophysical approach to what is referred to as “mental chronom- etry” [50–52], which uses measurements of the time between a stimulus onset and an immediate behavioral response to the stimulus. Hick’s Law [53,54], in particular, estab- lished on the basis of experiments in traditional sensory psychophysics, was repeatedly confirmed in studies by others [48–52]. The law directly relates response time to amount of information in the stimulus, and amount of information in the stimulus to uncertainty as a biologically grounded and potentially universal mechanism underlying sensation, perception, attention and, ultimately, decision [48–53]. In its most general form, Hick’s Law postulates that, provided the error rate in the given psychophysical task is low, RT increases linearly with the amount of transmitted information (I) in a set of signals or, as here in this study, a visual image configuration. The law extends to a direct relationship between choice RT and stimulus uncertainty (SU), as plotted graphically in Figure1 for illustration, and predicts that, provided the response error rate is low, RT increases linearly with stimulus uncertainty (SU) RT = a + b (SU) (1) Symmetry 2021, 13, x FOR PEER REVIEW 3 of 16 Symmetry 2021, 13, 299 3 of 15 Figure 1. Hick’s Law [53,54] postulates that, provided the error rate in the given psychophysical Figure 1. Hick’s Law [53,54] postulates that, provided the error rate in the given psychophysical task task is low, sensory system uncertainty (SU) increases linearly with the amount of transmitted is low, sensory system uncertainty (SU) increases linearly with the amount of transmitted information information (I) in a set (top graph). The law presumes a direct relationship between choice RT and sensory(I) in a set system (top graph uncertainty). The law (SU) presumes where RT a directincrea relationshipses linearly betweenwith amount choice of RT transmitted and sensory infor- system mation/stimulusuncertainty (SU) uncertainty where RT increases(bottom graph linearly). with amount of transmitted information/stimulus uncertainty (bottom graph). There is no evidence that RT in low-level visual decision tasks would be influenced There is no
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